I generated a 2d Gaussian noise then modulated it with a 2d cosine (f(x,y)=cos(2*pi/N*a*x)) witch oscillate only with the x direction and "a" is the frequency.

In a nutshell

N: Gaussian Noise size N*N

P: f(x,y)=cos(2*pi/N*a*x) a: frequency

I=P.N

after i take the Fourier transform of I, frequency pairs at offset (u,v) and (u+2a,v) have correlated phase.

If i do the experiment with another noise for example uniform noise (in Matlab: rand(N,N)) and then modulate it with the same cosine there

is no such correlations.

I want to what property of Gaussian noise cause this correlations?

Thank u all for help in advance.